CLAIM The ornamental design for a "clothing fastener accessory," as shown and described.

Description:

FIG. 1 is a left front perspective view of a new design for a clothing fastener accessory;

FIG. 2 is a top view;

FIG. 3 is a bottom view;

FIG. 4 is a side elevational view, the opposite side view being a mirror image thereof;

FIG. 5 is a top view showing the clothing fastener accessory as it may be applied over the female half of a snap button, the ghost lines are for the purpose of illustrating environment only; and,

FIG. 6 is a bottom view of the clothing fastener accessory shown in FIG. 5 as it attaches over the anchor portion of the snap button, the ghost lines are again for the purpose of illustrating the environment.